arXiv subjects
Publications and source records attributed to Matthias Burkardt.
We discuss some constraints on the $x$ and $t$-dependence of $E(x,0,t)$ that arise from positivity bounds in the impact parameter representation. In addition, we show that $E(x,0,0)$ for the nucleon vanishes for $x\to 1$ at least as rapidly as $(1-x)^4$. Finally we provide an inequality that limits the contribution from $E$ to the angular momentum sum rule.
We illustrate how an axial asymmetry in impact parameter dependent parton distributions can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. The single spin asymmetry arising from the asymmetry of the impact parameter dependent parton distributions is shown to exhibit a pure $\sin ϕ$ dependence.
Generalized parton distributions (GPDs) with purely transverse momentum transfer can be interpreted as Fourier transforms of the distribution of partons in impact parameter space. The helicity-flip GPD $E(x,0,-\Dps)$ is related to the distortion of parton distribution functions in impact parameter space if the target is not a helicity eigenstate, but has some transverse polarization. This transverse distortion can be used to develop an intuitive explanation for various transverse single spin asymmetries.
The Fourier transform of generalized parton distribution functions at xi=0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to the impact parameter distribution of unpolarized quarks for an unpolarized nucleon, H-tilde is related to the distribution of longitudinally polarized quarks in a longitudinally polarized nucleon, and $E$ is related to the distortion of the unpolarized quark distribution in the transverse plane when the nucleon has transverse polarization.
For an unpolarized target, the generalized parton distribution $H_q(x,0,t)$ is related to the distribution of partons in impact parameter space. The transverse distortion of this distribution for a transversely polarized target is described by $E_q(x,0,t)$.
We study how the components of hadronic wave functions in light-cone quantization depend on the ultraviolet cut-off by relating them in a systematic way to the matrix elements of a class of quark-gluon operators between the QCD vacuum and the hadrons. From this, we derive an infinite set of scale-evolution equations for the individual contributions to parton distributions from the Fock expansion. When summed over all the contributions, we recover the well-known DGLAP equation.
To appear in the proceedings of The Phenomenology of Large N(c) QCD, Tempe, Arizona, 9-11 Jan 2002.
The formalism for describing hadrons using a light-cone Hamiltonian of SU(N) gauge theory on a coarse transverse lattice is reviewed. Physical gauge degrees of freedom are represented by disordered flux fields on the links of the lattice. A renormalised light-cone Hamiltonian is obtained by making a colour-dielectric expansion for the link-field interactions. Parameters in the Hamiltonian are renormalised non-perturbatively by seeking regions in parameter space with enhanced Lorentz symmetry. In the case of pure gauge theories to lowest non-trivial order of the colour-dielectric expansion, this is sufficient to determine accurately all parameters in the large-N limit. We summarize results from applications to glueballs. After quarks are added, the Hamiltonian and Hilbert space are expanded in both dynamical fermion and link fields. Lorentz and chiral symmetry are not sufficient to accurately determine all parameters to lowest non-trivial order of these expansions. However, Lorentz symmetry and one phenomenological input, a chiral symmetry breaking scale, are enough to fix all parameters unambiguously. Applications to light-light and heavy-light mesons are described.
Chiral condensates in the trivial light-cone vacuum emerge if defined as short-time limits of fermion propagators. In gauge theories, the necessary inclusion of a gauge string in combination with the characteristic light-cone infrared singularities contain the relevant non-perturbative ingredients responsible for formation of the condensate, as demonstrated for the 't Hooft model.
We present results from a study of meson spectra and structure in the limit where one quark is infinitely heavy. The calculations, based on the framework of light-front QCD formulated on a transverse lattice, are the first non-perturbative studies of B-mesons in light-front QCD. We calculate the Isgur-Wise form factor, light-cone distribution amplitude, the heavy-quark parton distribution function and the leptonic decay constant of B-mesons.
I discuss the physical interpretation of GPDs in the limit $ξ=0$, where the $t$ dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also provides a physical interpretation for Ji's angular momentum sum rule.
Generalized parton distributions (GPDs) provide a link between form factors, parton distributions and other observables. I discuss the connection between GPDs and parton distributions as a function of the impact parameter. Since this connection involves GPDs in the limit of vanishing skewedness parameter $ξ$, i.e. when the off-forwardness is purely transverse, I also illustrate how to relate $ξ\neq 0$ data to $ξ=0$ data, which is important for experimental measurements of these observables.
The connection between parton distributions as a function of the impact parameter and off-forward parton distributions is discussed in the limit of vanishing skewedness parameter $ζ$, i.e. when the off-forwardness is purely transverse. For the $2^{nd}$ moment it is also illustrated how to relate $ζ\neq 0$ data to $ζ=0$ data, which is important for experimental measurements of these observables.
We present a number of exact relations for the heavy quark limit and develop an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the new results are relation 3μ_π^2=\barΛ^2 - m_{sp}^2+β^2, 1/m_Q corrections to the decay constants, to the kinetic expectation values and 1/m_Q^2 nonperturbative corrections to the B->D amplitude at zero recoil. The properties of the IW functions are addressed and the small velocity sum rules are verified.
We use two-dimensional QCD as a toy laboratory to study off-forward parton distributions (OFPDs) in a covariant field theory. Exact expressions (to leading order in $1/N_C$) are presented for OFPDs in this model and are evaluated for some specific numerical examples. Special emphasis is put on comparing the $x>ζ$ and $x<ζ$ regimes as well as on analyzing the implications for the light-cone description of form factors.
It is shown that off-forward parton distributions for $ζ=0$, i.e. where the initial and final state differ only in their transverse momenta, can be interpreted as a simultaneous measurement of the longitudinal momentum and transverse position (impact parameter) of partons in the infinite momentum frame.
In these notes, the transverse ($\perp$) lattice approach is presented as a means to control the $k^+\to 0$ divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the $\perp$ lattice motivate the color-dielectric formulation, where the link fields are linearized.
The $Q\bar{Q}$ potential is calculated in the Color-Dielectric Formulation of Transverse Lattice QCD. In such a formulation an effective potential is used to enforce the $SU(N_c)$ symmetry of the link fields. This effective potential is truncated at fourth order. Surprisingly, there is striking rotational invariance in the ground state $Q\bar{Q}$ potential as well as in the first hybrid mode.